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Archiv der Mathematik

, Volume 89, Issue 4, pp 296–297 | Cite as

On central automorphisms that fix the centre elementwise

  • Mehdi Shabani AttarEmail author
Article

Abstract.

Let G be a group and let Aut c (G) be the group of central automorphisms of G. Let \({{C_{{\rm Aut}_{c}(G)}}(Z(G))}\) be the set of all central automorphisms of G fixing Z(G) elementwise. In this paper we prove that if G is a finite p-group, then \({C_{{\rm Aut}_{c}(G)}}(Z(G))\) = Inn(G) if and only if G is abelian or G is nilpotent of class 2 and Z(G) is cyclic.

Mathematics Subject Classification (2000).

20D45 20E36 

Keywords.

Central automorphisms finite p-groups 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran

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